EFFECT OF TRANSVERSE CURVATURE ON AXISYMMETRIC COMPRESSIBLE LAMINAR BOUNDARY LAYER
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摘要: 在轴对称细长体的绕流中,同物体当地横向曲率半径相比,粘性边界层厚度可能不是一个小量,而可能是大好多倍的量;这时在经典的Prandtl边界层方程中,以物体的横向曲率半径来代替边界层中任一一点到对称轴的距离,这种简化方法已不适用.因此,本文老虑了横向曲率对轴对称可压缩层流边界层流动的影响.首先研究了强影响区.在完全气体,Prandtl数等于1,粘性系数与温度成正比,以及压力梯度可以忽略等假定下,以一个表示横向曲率影响的量θ为小参数,将流函数展成幂级数,从而求得了强影响区域中的摩阻系数和热传递系数的渐近解.为了使这个展开式一致有效,文中用FLK方法消除了二级近似(卽级数中的第三项少在物面附近的奇异性。结果表明,对于幂次物体rw~xn来说,在强影响区,物面摩阻系数Cf和热传递系数St有下面的形式:Cf=4Ce/Rex Tw/Te x/rw cosφ{θ+[0.577-In(1+2n)]θ2}+O(θ3,St=1/2Cf.其次,采用动量积分关系方法研究了横向曲率在整个流动区域中的影响,文中采用Crocco变量下的形式,选择适当的切应力τ和速度μ的关系,求得了圆柱和圆锥的Cf, St表达式,井与弱影响区、强影响区的渐近解作了比较.Abstract: The thickness of the boundary layer over an axisymmetric slender body may be comparable to, or even of several times the local radius of the transverse curvature of the body. The practice of replacing distance of a point in the boundary layer from the axis by the local body radius, as in classical Prandtl boundary layer equatiions,is then no longer applicable.The present work discusses the effcet of the transverse curvature on the axisymmetric compressiboe laminar boundary layer flow,analogous to the work of Lighthill and Glauert for the incompressible case.The first part of the paper deals with the strong effect region, i.e., the region where the boundary layer thickness is much larger than the local body radius.The usual assumptions of perfect gas, Prandtl number equal to one and linear viscosity-temperature relation are made.Neglecting the pressure gradient,one may find a small parameter ε to characterize the transverse curvature effect.The reduced stream function is then expressed as a power series of ε and the asymptotic solutions for skin friction and heat transfer rate are found.It is shown that the singularity of the second approximation(the third term in series)near the wall may be removed by using the PLK method and the solution is then uniformly valid.For power-lawed bodies,rw~xn,the skin friction coefficient Cf and the Stanton number St in the strong effect region may be expressed as Cf=4Ce/Rex Tw/Te x/rw cosφ{θ+[0.577-In(1+2n)]θ2}+O(θ3,St=1/2Cf In the second part, the transverse curvature effect in the entire flow field is investigated by means of momentum integral method where the Crocco's independent variables x,μ are used.With a suitable choice of a relation between shearing stress τ and velocity μ,approximate solutions for Cf and St of the circular cylinder and circular cone, valid for the entire range of transverse curvature paameters Ω and Φ,are found Coparison of the results with the Probstein and Elliott's serics solution for the weak effect region and the solution for the strong effect region found in the first part is made.
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Probstein, R, F, and Elliott, D., The transverse curvature effect in eompressi6le axially symmetric laminar boundary Payer flow, jour.Aero. Sci,23, 3, 1956, 208-224. Seban, R. A. and Bond, R., Skin-friction and heat transfer characteristics of a laminar boundary layer on“cylinder in axial incomfsressihle flaw, Jour. Aero. Sci,18, 10, 1951, 671-675. Kelly, H. R., A note an the laminar boundary layer on a circular cylinder in axial incompressible flow, Jour. Aero. Sci,21, 9, 1954, 534. Glauerr, M. B. and Z.igtrthill, M. J., The axisymmetric boundary layer on a long thin cylinder, Proc.Ray. Sac., 5rries A, 230, 1955, 188-203. Stewartson, K,The asymptotic boundary layer an a circular cylinder in axial incompressible flow, Quart. Appl, Math., 13, 2, 1955, 113-122. Bourne, D. E. and Ltavies, D. R., Heat transfer through the laminar boundary layer an“circular cylinder in axial incompressible flaw, Quart. Jour, of Mech. and Appl. Math., 11, 1, 1958, 52-66. Yasuhara, M., Axisymmetric viscous flaw past very slender bodies of revolution, jour. Aero. Sci,29, 5. 1962. 667-679. Rant, J.. Skin friction of slender cones in hypersonic flow, AIAA Jour., 2, 4, 1964, 755-756. Stewartson, K,Viscous hypersonic flow past a slender cone, Phys. of Fluids, 7, 5, 1964, 667-675. Wei, M. H., Asymptotic boundary layer over a slender body of revolution in axial compressible flow. AIAA Jour.. 3. 5. 1965. 809-816. Гиневский,А.С.,Солодкин,Е.Е.,Влияние поперечной кривизны поверхности на характеристики осесимметричного турбулентного пограничного слоя,ПММ,22,6,1958,819-825. Гиневский,А.С.,Солодкин,Е.Е.,Влияние поперечной кривизны поверхности на характеристики неизотермического осесимметричного турбулентного пограничного слоя сжимаемого чаза,Изб,АН СССР,ОТН,Мех.ц Мащ.,1,1963,66-110. 钱学森(Tsien, H. S),The Poincaré-Lighthill-Kuo Method, in "Advances in Appl.Mech.", Vol. IV. Academic Press. New York.1956,281-349. -
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